4,202 research outputs found
Improvement of stabilizer based entanglement distillation protocols by encoding operators
This paper presents a method for enumerating all encoding operators in the
Clifford group for a given stabilizer. Furthermore, we classify encoding
operators into the equivalence classes such that EDPs (Entanglement
Distillation Protocol) constructed from encoding operators in the same
equivalence class have the same performance. By this classification, for a
given parameter, the number of candidates for good EDPs is significantly
reduced. As a result, we find the best EDP among EDPs constructed from [[4,2]]
stabilizer codes. This EDP has a better performance than previously known EDPs
over wide range of fidelity.Comment: 22 pages, 2 figures, In version 2, we enumerate all encoding
operators in the Clifford group, and fix the wrong classification of encoding
operators in version
Toward fault-tolerant quantum computation without concatenation
It has been known that quantum error correction via concatenated codes can be
done with exponentially small failure rate if the error rate for physical
qubits is below a certain accuracy threshold. Other, unconcatenated codes with
their own attractive features-improved accuracy threshold, local
operations-have also been studied. By iteratively distilling a certain
two-qubit entangled state it is shown how to perform an encoded Toffoli gate,
important for universal computation, on CSS codes that are either
unconcatenated or, for a range of very large block sizes, singly concatenated.Comment: 12 pages, 2 figures, replaced: new stuff on error models, numerical
example for concatenation criteri
Quantum Teleportation is a Universal Computational Primitive
We present a method to create a variety of interesting gates by teleporting
quantum bits through special entangled states. This allows, for instance, the
construction of a quantum computer based on just single qubit operations, Bell
measurements, and GHZ states. We also present straightforward constructions of
a wide variety of fault-tolerant quantum gates.Comment: 6 pages, REVTeX, 6 epsf figure
Robust polarization-based quantum key distribution over collective-noise channel
We present two polarization-based protocols for quantum key distribution. The
protocols encode key bits in noiseless subspaces or subsystems, and so can
function over a quantum channel subjected to an arbitrary degree of collective
noise, as occurs, for instance, due to rotation of polarizations in an optical
fiber. These protocols can be implemented using only entangled photon-pair
sources, single-photon rotations, and single-photon detectors. Thus, our
proposals offer practical and realistic alternatives to existing schemes for
quantum key distribution over optical fibers without resorting to
interferometry or two-way quantum communication, thereby circumventing,
respectively, the need for high precision timing and the threat of Trojan horse
attacks.Comment: Minor changes, added reference
Controlling qubit transitions during non-adiabatic rapid passage through quantum interference
In adiabatic rapid passage, the Bloch vector of a qubit is inverted by slowly
inverting an external field to which it is coupled, and along which it is
initially aligned. In non-adiabatic twisted rapid passage, the external field
is allowed to twist around its initial direction with azimuthal angle \phi(t)
at the same time that it is non-adiabatically inverted. For polynomial twist,
\phi(t) \sim Bt^{n}. We show that for n \ge 3, multiple qubit resonances can
occur during a single inversion of the external field, producing strong
interference effects in the qubit transition probability. The character of the
interference is controllable through variation of the twist strength B.
Constructive and destructive interference are possible, greatly enhancing or
suppressing qubit transitions. Experimental confirmation of these controllable
interference effects has already occurred. Application of this interference
mechanism to the construction of fast fault-tolerant quantum CNOT and NOT gates
is discussed.Comment: 8 pages, 7 figures, 2 tables; submitted to J. Mod. Op
Quantum Fourier transform revisited
The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a particular matrix decomposition of the discrete Fourier transform (DFT) matrix. In this paper, we show that the quantum Fourier transform (QFT) can be derived by further decomposing the diagonal factors of the FFT matrix decomposition into products of matrices with Kronecker product structure. We analyze the implication of this Kronecker product structure on the discrete Fourier transform of rank-1 tensors on a classical computer. We also explain why such a structure can take advantage of an important quantum computer feature that enables the QFT algorithm to attain an exponential speedup on a quantum computer over the FFT algorithm on a classical computer. Further, the connection between the matrix decomposition of the DFT matrix and a quantum circuit is made. We also discuss a natural extension of a radix-2 QFT decomposition to a radix-d QFT decomposition. No prior knowledge of quantum computing is required to understand what is presented in this paper. Yet, we believe this paper may help readers to gain some rudimentary understanding of the nature of quantum computing from a matrix computation point of view
Immunity of information encoded in decoherence-free subspaces to particle loss
We demonstrate that for an ensemble of qudits, subjected to collective
decoherence in the form of perfectly correlated random SU(d) unitaries, quantum
superpositions stored in the decoherence free subspace are fully immune against
the removal of one particle. This provides a feasible scheme to protect quantum
information encoded in the polarization state of a sequence of photons against
both collective depolarization and one photon loss, and can be demonstrated
with photon quadruplets using currently available technology.Comment: to appear in Phys. Rev. A; 5 pages, 2 figures; content changed a bit
(the property demonstrated explicitly on a 4 qubit state
Efficient discrete-time simulations of continuous-time quantum query algorithms
The continuous-time query model is a variant of the discrete query model in
which queries can be interleaved with known operations (called "driving
operations") continuously in time. Interesting algorithms have been discovered
in this model, such as an algorithm for evaluating nand trees more efficiently
than any classical algorithm. Subsequent work has shown that there also exists
an efficient algorithm for nand trees in the discrete query model; however,
there is no efficient conversion known for continuous-time query algorithms for
arbitrary problems.
We show that any quantum algorithm in the continuous-time query model whose
total query time is T can be simulated by a quantum algorithm in the discrete
query model that makes O[T log(T) / log(log(T))] queries. This is the first
upper bound that is independent of the driving operations (i.e., it holds even
if the norm of the driving Hamiltonian is very large). A corollary is that any
lower bound of T queries for a problem in the discrete-time query model
immediately carries over to a lower bound of \Omega[T log(log(T))/log (T)] in
the continuous-time query model.Comment: 12 pages, 6 fig
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